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We provide a microscopic theory for the Doppler velocimetry of spin propagation in the presence of spatial inhomogeneity, driving electric field and the spin orbit coupling in semiconductor quantum wells in a wide range of temperature regime based on the kinetic spin Bloch equation. It is analytically shown that under an applied electric field, the spin density wave gains a time-dependent phase shift $phi(t)$. Without the spin-orbit coupling, the phase shift increases linearly with time and is equivalent to a normal Doppler shift in optical measurements. Due to the joint effect of spin-orbit coupling and the applied electric field, the phase shift behaviors differently at the early and the later stages. At the early stage, the phase shifts are the same with or without the spin-orbit coupling. While at the later stage, the phase shift deviates from the normal Doppler one when the spin-orbit coupling is present. The crossover time from the early normal Doppler behavior to the anomalous one at the later stage is inversely proportional to the spin diffusion coefficient, wave vector of the spin density wave and the spin-orbit coupling strength. In the high temperature regime, the crossover time becomes large as a result of the decreased spin diffusion coefficient. The analytic results capture all the quantitative features of the experimental results, while the full numerical calculations agree quantitatively well with the experimental data obtained from the Doppler velocimetry of spin propagation [Yang {it et al.}, Nat. Phys. {bf 8}, 153 (2012)]. We further predict that the coherent spin precession, originally thought to be broken down at high temperature, is robust up to the room temperature for narrow quantum wells. We point out that one has to carry out the experiments longer to see the effect of the coherent spin precession at higher temperature due to the larger crossover time.
Spin-orbit (SO) interactions give a spin-dependent correction r_so to the position operator, referred to as the anomalous position operator. We study the contributions of r_so to the spin-Hall effect (SHE) in quasi two-dimensional (2D) semiconductor
We theoretically study the coherent nonlinear response of electrons confined in semiconductor quantum wells under the effect of an electromagnetic radiation close to resonance with an intersubband transition. Our approach is based on the time-depende
In the absence of an external field, the Rashba spin-orbit interaction (SOI) in a two-dimensional electron gas in a semiconductor quantum well arises entirely from the screened electrostatic potential of ionized donors. We adjust the wave functions o
Experimental and theoretical studies of all-optical spin pump and probe of resident electrons in CdTe/(Cd,Mg)Te semiconductor quantum wells are reported. A two-color Hanle-MOKE technique (based on continuous-wave excitation) and time-resolved Kerr ro
At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a